Automation 2017: Innovations in Automation, Robotics and by Roman Szewczyk, Cezary Zieliński, Malgorzata Kaliczyńska

By Roman Szewczyk, Cezary Zieliński, Malgorzata Kaliczyńska

This booklet contains papers offered at Automation 2017, a global convention held in Warsaw from March 15 to 17, 2017. It discusses study findings linked to the ideas in the back of 4.0, with a spotlight on delivering a greater knowing of and selling participation within the Fourth business Revolution. every one bankruptcy offers a close research of a particular technical challenge, typically by means of a numerical research, simulation and outline of the result of imposing the answer in a real-world context. The theoretical effects, functional suggestions and instructions provided are helpful for either researchers operating within the zone of engineering sciences and practitioners searching for strategies to business problems.

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1. 15) we have 2 1 0 À2 3 2 0 1 1 3 7 2 0 5; À1 0 2 2 3 x2 ðtÞ þ u1 ðtÞ þ u32 ðtÞ   f11 ðxðtÞ; uðtÞÞ 6 7 f ðxðtÞ; uðtÞÞ ¼ ¼4 x31 ðtÞ þ u21 ðtÞ 5; f12 ðuðtÞÞ 2 u1 ðtÞ þ u2 ðtÞ 6 E ¼ 40 0 0 0 6 7 1 5; A ¼ 4 1 0 0 ð3:16Þ gðxðtÞ; uðtÞÞ ¼ ½x1 ðtÞ þ 2x22 ðtÞ þ x3 ðtÞ þ u21 ðtÞ þ u2 ðtÞ þ 3u32 ðtފ: Performing on the Eq. 16) the elementary row operation L½1 þ 2  2Š we obtain the Eq. 3) with     0 2 5 1 ; A11 ¼ ; A12 ¼ ½ 0 À1 0 Š; 1 1 2 0 " # 2x31 ðtÞ þ x22 ðtÞ þ u1 ðtÞ þ 2u21 ðtÞ þ u32 ðtÞ f11 ðxðtÞ; uðtÞÞ ¼ ; f12 ðuðtÞÞ ¼ ½u1 ðtÞ þ u22 ðtފ: x31 ðtÞ þ u21 ðtÞ 1 E1 ¼ 0 0 0 ð3:17Þ Note that the matrix Descriptor Positive Nonlinear Systems  E1 A12  2 1 ¼ 40 0 0 0 1 3 0 15 0 43 ð3:18Þ is nonsingular and in this case we obtain the Eq.

6). Assuming regular pencil, after q steps we obtain a nonsingular matrix [15]  Eq ÀAq þ 1  ð3:9Þ which lead to following differential equation a qa d a xðtÞ    0 uðtÞ þ B  1 d uðtÞ þ . . þ B  q d uðtÞ ¼ AxðtÞ  uðtÞ; ¼ AxðtÞ þ B þ B dta dta dtqa ð3:10Þ where ¼ A  Eq ÀAq þ 1  ¼ ½B 0 B 1 B À1  Aq 0  ; 0 ¼ B   q Š 2

Sci. 14(1), 19–23 (2004) 13. : Linear Control Systems, vol. 1. Wiley, New York (1992) 14. : Polynomial and Rational Matrices: Applications in Dynamical Systems Theory. Springer, London (2007) 15. : Positive 1D and 2D Systems. Springer, London (2002) 16. : Positive linear systems with different fractional orders. Bull. Pol. Acad. Sci. Techn. 58(3), 453–458 (2010) 17. : Positivity of descriptor linear systems with regular pencils. Arch. Electr. Eng. 61(1), 101–113 (2012) 18. : Positivity and asymptotic stability of descriptor linear systems with regular pencils.

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